A Catalan surface all straight line generators of which intersect a fixed straight line, called an axis of the conoid. For example, a hyperbolic paraboloid is a conoid with two axes.
The position vector of a conoid is given by
where is a unit vector having the same direction as an axis of the conoid and is some function. For a right conoid , , and then its axis is a line of striction. A right conoid with is a helicoid.
|[a1]||M. Berger, B. Gostiaux, "Géométrie différentielle: variétés, courbes et surfaces" , Presses Univ. France (1987)|
|[a2]||M.P. Do Carmo, "Differential geometry of curves and surfaces" , Prentice-Hall (1976)|
Conoid. I.Kh. Sabitov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Conoid&oldid=18035